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If a vertical line, within the domain of the function, intersects the graph in more than one points, it is not a function.
The domain of a function is simply the x values of the function
Find the maximum and minimum values that the function can take over all the values in the domain for the input. The range is the maximum minus the minimum.
The "x values that work are the domain numbers like for y=x+1 would be any real number. But, y= sqrx x would have to be non-negative.
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.